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PRELOADED PARABOLIC DISH ANTENNAS FOR THE SQUARE KILOMETER ARRAY

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					PRELOADED PARABOLIC DISH ANTENNAS FOR
     THE SQUARE KILOMETER ARRAY




                 Govind Swarup
    National Centre for Radio Astrophysics
    Tata Institute of Fundamental Research
             Pune – 411 007, India




                       And




             N. Udaya Shankar
          Raman Research Institute
          Bangalore-560 080, India




                  th
                17 June 2002




                        1
                              Table of Contents



No.           Contents                                              Page No.
       Summary                                                         3
 1.    Introduction                                                    4
 2.    Basic design aspects of the Preloaded Parabolic Dish (PPD)      6
       antenna


 3.    Detailed description of the 12 m Preloaded Parabolic Dish       7
       antenna

 3.1   Design Procedure                                                7
 3.2   Details of the 12 m PPD antenna                                11


 4.    Procedure for fabrication of the 12 m Preloaded Parabolic      12
       Dish (PPD) antenna

 5.    Antenna mount & drive system for the 12 m Preloaded            14
       Parabolic Dish antenna

 6.    Strawman’s design for the antenna system of SKA using          14
       8343 nos. of 12 m PPDs.

 7.    Discussions                                                    16
 7.1   Advantages of Preloaded Parabolic Dishes                       16
 7.2   Antenna element for SKA                                        16


 8.    Conclusion                                                     17
 9.    Acknowledgement                                                17
 10.   References                                                     18
       Tables 1 to 4                                                  19
       Figures 1 to 4                                                 23




                                         2
   PRELOADED PARABOLIC DISH ANTENNAS FOR THE SQUARE KILOMETER
                             ARRAY


                                     Govind Swarup
                        National Centre for Radio Astrophysics
                        Tata Institute of Fundamental Research
                                   Pune-411 007, India

                                            And

                                  N. Udaya Shankar
                               Raman Research Institute
                               Bangalore-560 080, India




SUMMARY

       A novel and economical concept has been developed for a parabolic dish
antenna, which can provide a very large collecting area, over a wide frequency range,
for SKA at an affordable cost.         The backup structure of the parabolic dish is
considerably simplified by preloading its structural members.        A set of high tensile
tubular members are clamped rigidly to a central hub, bent elastically to lie close to a
parabolic curve and then bolted at the far end to the same number of straight tubular
members placed circumferentially along the rim of the dish. A similar number of straight
structural members are also clamped circumferentially at one or more intermediate
locations.   This results in a rigid framework of the backup structure of a preloaded
parabolic dish (PPD) antenna. It is important to note that all the structural members are
suitably prestressed in order to store in them sufficient initial elastic energy for enabling
them to resist gravitational and wind forces under operational and survival wind




                                             3
conditions. The preloaded design minimizes inertia and wind loads on the dish. It also
allows rapid fabrication of the antenna. Static and dynamic finite element analysis has
been made to develop a detailed design of a 12 m dish. Preliminary studies have also
been made for a 25 m dish.


       A 12 m diameter preloaded parabolic dish antenna has been fabricated at the
Raman Research Institute (RRI), Bangalore. Its reflecting surface consists of panels
made of welded stainless steel wire mesh of size 6 mm x 6 mm x 0.55 mm with rms
error of about 2 mm. Therefore, the 12 m dish is expected to operate upto about 10
GHz although with a reduced efficiency at the highest frequency. Economical designs
are now being developed by RRI for the mechanical and servo drive system of the 12 m
dish which will be fully fabricated and tested by mid 2003. Present cost estimate for
8000 nos. of fully steerable preloaded parabolic dish antennas of 12 m or 5000 nos. of
15 m diameter for operation upto about 10 GHz is about US $ 500 million. Possibility of
extending its operation from 30 MHz to 22 GHz is also discussed briefly in this report.


       The new concept of the “Preloaded Parabolic Dish antenna and the Method of
Making It” is described in detail for a 12 m diameter dish, as an example, in the Patent
application No. 721/MUM/2000 dated 1st August 2000 filed in India by Swarup and
Tapde, and Patent application No. PCT/IN 01/00137 dated 30th July 2001 filed by the
above authors under the International Patent Corporation Treaty (PCT) of the World
Patent Intellectual Organization (WIPO) & published as reference No.WO 02/13314 A2
dated 14.02.2002/Serial 1806 (www.WIPO.org)


1.     Introduction
       It is indeed a very challenging task to design an economical antenna system for
the Square Kilometer Array [ 1 ] for covering a wide frequency range, good polarization
characteristics, low system temperature and steerability over a large area of the sky.


       Parabolic dishes have been used quite widely for the antenna system of radio
telescopes as they have point focus, which makes it possible to obtain low system
temperature and good polarization characteristics over a wide frequency range. Also, it
is possible to cover a large area of the sky. However, conventional designs of parabolic


                                            4
dishes are quite expensive, e.g. the cost of each of the ten 25 m parabolic dish
antennas of the Very Long Base Line Array (VLBA) using accurate Al panels for the
                                                                               2
reflecting surface, was about US $ 2.3 million in 1987 (about $ 5000/m ). The VLBA
dishes can operate upto about 44 GHz. The present cost of a VLBA type antenna is
likely to be about US $ 4 million. The cost of a parabolic dish antenna of diameter d is
                         -2.5-2.7
expected to scale as d              , as has been suggested empirically by many workers. The
cost also depends upon the shortest wavelength of operation, perhaps scales as λ
                                                                                        -0.25
                                                                                                for
a similar basic design, but using stiffer back up structure, and Al panels and
mechanical/electrical drive system of higher tolerance. It may be noted that the back-up
structure of conventional parabolic dishes, as well as GMRT, are quite labour intensive
as they require considerable effort in assembly and welding of the structural members.


       Being located outdoors, parabolic dishes are subjected to large forces due to
wind and must be designed for survival wind velocities.         Force, F, due to wind is given
by F = p.A. Cd, where p is pressure of wind, A is area and Cd is drag factor. For a
parabolic dish antenna with the reflecting surface panels made of solid Al sheet, Cd ~ 2.
Actually wind forces and torques depend on the orientation of the dish [ 2 ].               For
reflecting surface made of wire mesh, the value of Cd for the dish can be decreased to =
0.25 - 0.3, depending upon the wire mesh size.


       For the 30 Nos. of 45 m diameter parabolic dishes of the Giant Metrewave Radio
Telescope (GMRT) [ 3 ] , we used a so called `SMART’ design, i.e. Stretched Wire
Mesh Attached to Rope Trusses. The mesh size is 10 mm x 10 mm, 15 mm x 15 mm
and 20 mm x 20 mm for the inner, middle and outer one-third area of the GMRT
parabolic dishes. The mesh is made of stainless steel wire of 0.55 mm diameter and is
made in automatic machines using resistive arc welding. The cost of each of the 45 m
diameter dish was about US $ 300,000 at 1993 prices. Although labour cost is much
lower in India, material cost is higher in India than prevalent internationally.           The
possibility of using GMRT type design for SKA is discussed by Swarup [ 4 ].


        In order to further simplify the backup structure of a parabolic dish antenna, a
novel concept of preloading its structural members has been developed, and it is called
as Preloaded Parabolic Dish Antenna (PPD). The members of the PPD are mostly


                                                  5
bolted and thus minimize the labour involved in its assembly. It is important to note that
all the structural members are provided suitable prestress in order to store in them
sufficient internal strain energy so that their stresses remain within the specified bounds
as per the national codes for structures under conditions of the specified operational and
survival wind velocity.


       The basic principle of the Preloaded Parabolic Dish antenna is described in
Section-2. In Section-3 are given details of a 12 m parabolic dish which has been
fabricated and assembled at the Raman Research Institute (RRI), Bangalore.             The
detailed design of the 12 m PPD antenna is based on computer calculations made by
Professor Ashok Joshi of the Indian Institute of Technology, Mumbai. Prof. Joshi has
also made a preliminary design of a 25 m PPD antenna and results are also
summarized in Section-3.      Procedures used for fabrication of the 12 m dish         are
described in Section-4.


       The mount for the 12 m dish and its mechanical and electrical (Servo) system is
being developed by the Raman Research Institute and different concepts being
examined by a Consulting Engineering             firm are briefly discussed in Section-5.
Preliminary estimates have been made for the cost of the mount and drive system which
seems to form a major part of the PPD antenna.


       A Strawman’s design for the SKA using Preloaded Parabolic Dish Antenna is
described in Section-6 including preliminary cost estimates. Discussions are given in
Section-7 and Conclusions in Section-8.


2.     Basic design aspects of the Preloaded Parabolic Dish (PPD) Antenna


       The preloaded concept is based on the principle that if a structure has an initial
stored strain energy, then under certain conditions it has the capacity to offer a large
stiffness to additional external loads. In the present invention this concept has been
applied to the design of the backup support structure of a dish antenna in order to
reduce its weight while retaining the required stiffness properties.




                                             6
       In the preloaded parabolic dish (PPD) antenna several straight radial members
are supported on a central hub and are bent by a normal force at their tips, which
generates bending strain energy in each of the members. A large number of such
members are bent and then connected to each other at their tips through straight tubular
members placed circumferentially at the rim of the dish which prevent the springback of
the bent members. Thus, a skeleton of the bent radial members that are prestressed by
the bending load applied by the rim members at their tips, is obtained which resembles
the configuration of a parabolic dish. By selecting a suitable geometry, the curvature of
each of the elastically bent radial members is made nearly the same as the curvature of
the required parabolic dish antenna at its location.   The amount of bending (or the
preload stress) is greater than or equal to the maximum stress that is expected to be
carried by the radial members under the survival wind conditions. Such a structural
configuration shows enhanced insensitivity to the external gravitational and wind loads
due to storage of internal strain energy. For obtaining additional rigidity against wind
and gravitational forces and also vibrational instabilities, the radial members are also
connected to one or more sets of bracing structural members at intermediate locations.


       In order to minimize wind loads on the structural members, it is preferred to use
tubes or pipes for the structural members which have low wind drag factor, Cd.


       The reflector panels that are light in weight and also have low wind loading are
fabricated by means of making stainless steel frames using thin tubes or channels and
then fixing welded wire mesh of appropriate mesh size and made of stainless steel wires
of suitable diameter depending upon the highest frequency of operation of the preloaded
parabolic dish.


       Alternatively, the conventional reflector panels made of solid or perforated metal
or metallized-plastic sheets are used. One may use panels made of metal sheets or
pressed parabolic dish for the central part of the preloaded parabolic dish, and wire
mesh or perforated sheets for the outer part in order to reduce wind loads yet allow
operation upto about 22 GHz.


3.     Detailed Description of the 12 m Preloaded Parabolic Dish Antenna.


                                           7
3.1    Design Procedure


       Fig. 1 (a) shows a single structural member that is bent by a preload Ps . After
the bending, the tip of the structural member is anchored to a stationary point `S’, with
the help of another elastic member. At this point the preload is removed, which results
in the relaxed shape of the structural member but results in the tensile straining of the
Anchor member. However, as the Anchor member is fairly rigid in the axial direction,
there is no significant reduction in the preload and the combined system attains an
internal elastic equilibrium (Fig. 1(b). In the preloaded parabolic dish, the above
anchoring is provided by the circumferential rim members which are considered fairly
rigid in the axial direction of the tube and this is the actual configuration of the backup
structure of the parabolic dish antenna under the zero wind condition.


       It may be noted that when the wind forces act from the front (concave) side of
the dish, its shape will be maintained because the rim and bracing members which are
fairly rigid, will take all the wind load and the radial members will act as simply supported
beams with marginal distortion of their shape. In the event of wind coming from the
back (convex) side, the dish will retain its original shape as long as the kinetic energy of
the wind forces is less than the stored internal strain energy. In fact this is used to
decide the amount of preload strain energy in order to ensure that this condition is
always satisfied. However, in case wind forces do exceed the preload, the difference is
supported by the rim and bracing members which can take significant amount of
compressive load and prevents any significant distortion of the shape of the dish.
Finally, it may be noted that while the primary intention of preload is to provide an initial
strain energy, the process of bending the radial members results in a curve which is
nearly a parabola. This gives the additional advantage of eliminating the process of
separately forming the parabola and, thus, reduces the overall fabrication cost of the
antenna.


       In Fig. 2 is shown details of a preloaded parabolic dish antenna of a 12 m
circular diameter. The preloaded antenna consist of a hub, curved radial members,
straight rim members of the outer circumferential ring, straight bracing members of the


                                             8
intermediate circumferential ring, a quadripod, inner ring     and reflector panels. The
radial members , rim members and bracing members are joined together rigidly using
clamps, joints and other gadgets. Inside the hub the antenna has inner curved radial
members connected to a ring at the centre.


       The back-up structure of a parabolic dish incorporates a hub for the purpose of
its connection to a drive system mounted on a yoke and a tower for supporting the dish.
In practice, the diameter of the hub varies from about 1/4 to 1/2 of the diameter of the
dish. In the present example, the hub has a diameter of 4m i.e. 1/3rd of the dish
diameter. The design of the inner parabolic dish between its apex and hub is relatively
straight forward and is based on conventional practice.


       It may be noted that the rim members connected at the periphery of the dish and
also the bracing members at intermediate positions of the radial members form a
polygon, as all these members are straight structural members. Since there are 24
radial members, the polygon is nearly circular for all practical purposes.


       For the said 12 m diameter parabolic dish described in this embodiment, a
welded wire mesh was selected for the reflecting surface for minimizing the wind loads,
which results in considerable economy. The wire mesh has a size of 6 mm x 6 mm and
consists of stainless steel wire of 0.55 mm diameter which allows operation of the dish
upto about 10 GHz. Finer wire mesh or perforated metal sheets or metallic plates may
be used for operation at higher frequencies. One may use panels made of metal sheets
or a pressed parabolic dish for the central part of the dish and wire mesh or perforated
sheets for the outer part in order to reduce wind loads yet allow operation upto about 22
GHz.


       It may be mentioned that the initial setting angle, θh , of the radial members at
the hub is an important parameter that affects (1) the magnitude of the preload and (2)
the deviation between the shape of the bent radial members and the exact parabola.
Further, it is to be mentioned here that if preloading of the radial members is to be
reduced, pre-curved radial members can be used which reduce the extent of the elastic
deformation and the preload or prestress. However, then the advantage of the stored


                                             9
internal strain energy is lost to some extent and it is necessary to understand the trade-
off between these two for deciding to use the straight or the pre-curved radial members.
Finally, the design of the radial member is subject to the condition that the deformed
shape must always lie below the exact parabola because the deviations then can be
exactly covered using adjustable bolts, leading to a fairly close match of the reflector
surface with the exact paraboloidal surface. A detailed finite element stress analysis of
the entire back-up structure including the hub, radial members, rim members, bracing
members, quadripod, and reflector panels            under the maximum load conditions,
corresponding to the dish facing horizon and the maximum wind (150 kmph) coming
from the front and the back, has been carried out for the 12 m dish and it was decided to
                                           2
use high tensile (yield strength 60 kg/mm ) radial tubular members of 40 mm diameter
and 8 mm wall thickness. In the analysis carried out, both the wind load and the dead
load are added in a scalar sense and it is seen that the effective stress due to wind
loads is of the order of 73% of the allowable stress at the survival wind speeds. The
allowable stress is taken as 85% of the yield strength. It may be recalled here that the
prestress is of the order of 95% of the allowable stress which indicates that the
maximum wind kinetic energy at 150 kmph is only about 75% of the stored internal
strain energy of the radial members in the form of prestress. Thus, there is about 20%
margin for the stress before rim members go slack and go in compression.         There is
no significant increase in the stress of the radial members because they are effectively
anchored in the rim members and bracing members.

       The circumferentially located straight rim members have the important function
of connecting the adjacent tips of all the 24 parabolic radial members. These rim
members also prevent the springback of the pre-stressed radial members, besides
providing the hoop mode strength to the dish structure. However, as the radial member
is a large member, it can bend significantly between its two end points (i.e. one end at
the tip and the other end at the hub), in addition to the requirement of quadripod being
supported on the radial member which can cause additional deformations. All these
have the potential to increase the dish distortion to unacceptable levels under the
operational conditions and in order to reduce this distortion, the intermediate bracing
members are provided for the 12 m dish.




                                               10
       The intermediate bracing members together with the hub and the rim members,
divide the total outer dish into radially two equal parts. It is seen that when the radial
members try to bend inwards (dish overall closing mode), the rim members and bracing
members go into compression and when the radial members try to bend outward (dish
overall opening mode), these members go into tension so that the overall dish distortion
is minimized. It may be mentioned here that these rim members and bracing members
do not play any role in the dish overall pure twisting mode as they undergo in-plane rigid
body rotation in this mode of elastic deformation and in this case only the radial
members provide the total twisting stiffness to the dish. For the 12 m dish although the
rim members and the bracing members are subjected to smaller loads than that of the
radial members, but the tube diameter of 40 mm and wall thickness of 8 mm is chosen
for these members also. This is also considered adequate for the purpose of resisting
compressive loads in the dish closing mode.

       A finite element analysis was also carried out for determining the natural
frequencies and mode shapes of the 12 m dish as described herein. The boundary
conditions were taken as four point clamped supports at the hub. The lowest natural
frequency of the vibration of the disk was 1.49 Hz for inplane bending mode (ovalling)
and is considered satisfactory.

       The difference in the shape of the elastically bent radial member and the exact
parabolic curve can be compensated suitably by using adjustable bolts             and is,
therefore, not a cause for concern in the design of the preloaded parabolic dish and is
also not treated as an error, but only as a deviation which is to be adjusted. The
parabolic reflector surface is required to be assembled from the wire mesh panels
which are made of stainless steel wire mesh tack welded by resistive arc welding to a
metallic frame attached to mounting plates.

3.2    Details of the 12 m PPD antenna

       The said 12 m diameter preloaded parabolic dish antenna consists of 24 radial
tubular members and has a focal length of 4.8 m (Fig. 2). The said 12 m dish has been
designed for a survival wind velocity of 150 kmph. The radial members are connected
to a hub of 4 m diameter made out of welded mild steel plates of 8 mm thickness and



                                           11
its cross-section has a width w1 = 200 mm and height of H = 200 mm. (Fig. 2). The
radius of the inner ring, hub, intermediate     circumferential bracing ring   and outer
circumferential ring (rim) are 600 mm, 2000 mm, 4000 mm and 6000 mm respectively.
In Fig. 3 the dotted line shows schematically location and inclination of the radial
members before their elastic bending; the broken line shows the elastically bent radial
tube and the full line the required parabola. It is found that the deviation of the curved
radial members from the parabola lies within ± 40 mm, which can be compensated by
using adjustable bolts. The radial, rim and bracing members consist of high tensile
seamless tubes of 40 mm diameter and 8 mm wall thickness, with a yield strength of 60
       2
kg/mm .      Alternatively tubes of 50 mm dia and 6 mm thickness may also be used.
Quadripod consists of seamless tubes of 50 mm dia and 8 mm wall thickness. The
reflecting panels are made of stainless steel welded wire mesh with a size of 6 mm x 6
mm (distance between adjacent wires of 6 mm) and wire diameter of 0.55 mm.

       The total weight of the 12 m diameter preloaded parabolic dish including weight
of the hub, various structural members, clamps and joints and the reflecting panels is
about 2.5 tonnes. For wind velocity of 150 kmph, the dish is subject to a wind force of
2.7 tonnes when facing to horizon and the wind torque about the elevation axis is 3
tonne m .      The dead load torque about the elevation axis is 4.7 tonne-m,       before
balancing of the dish by a counter weight. The frequency of the lowest vibrational mode
is 1.5 Hz.

       Calculations have also been made for a preloaded parabolic dish antenna of 25
m diameter for a survival wind velocity of 140 kmph. The 25 m dish has a total weight of
14 tonnes, wind force (horizon) 13 tonnes, wind torque about elevation axis of 19 tonne-
m and dead load torque (before balancing) of 42 tonne-m. These weights and torques
are much lower than those for conventional dishes. Calculated values for the 12 m and
25 m dishes are summarized in Table-1.


       Thus it has been shown that application of preload to the structural members as
well as the selection of an optimum configuration results in considerable reduction in the
weight and wind torques on the drive system of a parabolic dish and minimizes the
labour required for assembly including welding and bolting of          various structural



                                           12
members compared to that of a conventional back up structure, thus leading to
considerable economy.


4.     Procedure for Fabrication of the 12 m Preloaded Parabolic Dish Antenna


       Firstly, the hub of 4 m diameter with a cross section of 200 mm x 200 mm is
made of 8 mm plates and its top surface is machined. The hub is mounted on four
temporary pillers by clamping on four legs of the hub.       Next, 24 nos. of hub mounting-
pads    are bolted at equal circumferential distances on the hub (in case of mass
production, can be welded during fabrication of the hub). All the 24 nos. of radial
members     are then connected rigidly by clamping on the mounting-pads. Using a
theodolite placed at the centre of the parabolic dish, it is ensured that the tips of all the
24 nos. of radial members lie at equal angular distances and are in one horizontal
plane. The radial members are then bent elastically by applying a force with an
effective normal component at their tips using steel ropes and turnbuckles attached to
a ring-plate supported on a vertical tower connected on the hub             which is erected
temporarily to lie along the central axis of the 12 m parabolic dish. The ring can also be
made to rise gradually upto the plane of the rim using ropes and turn buckles.
Alternatively, for mass production, jacks supported on the ground or pullers supported
on the roof of a construction shed can be used.       Each of the radial members       is bent
elastically to a specified height from the `x’ axis of the parabola in the `y’ direction, (Fig.
3) using a theodolite placed at the centre of the dish and thus the radial members get
pre-stressed or preloaded to a calculated value.


       Radial members are then interconnected to straight bracing members of the
intermediate circumferential ring using bracing joints. Adjustment bolts of the bracing
members (say, on 4 out of 24 bracing members) are adjusted, if required to ensure that
the intermediate ring is rigidly connected to the radial members. Next, the tips of the
radial members are rigidly connected to the rim members using the rim joints at the
periphery of the dish.     Next, the steel ropes     and turn buckles      are loosened and
adjustments made using adjustment-bolts of the rim members                to ensure that the
circumferentially placed rim members        get rigidly connected to the radial members.
Next the central tensioning tower is removed and the quadripod            is mounted on the


                                              13
radial members at the location of the bracing members of the intermediate ring using
the quadripod flange. Next panel-mounting gadgets for mounting the reflector panels,
are attached to the radial members. The length of adjustable bolts of these gadgets is
adjusted using a centrally placed theodolite to ensure that the heights of the mounting
plates for bolting the reflector panels lie along the desired parabolic curve within a
tolerance of ± 0.5 mm. The reflector panels are then mounted on mounting plates and
surface accuracy is then measured using the theodolite. Suitable adjustments are made
in order to ensure that the reflecting surface lies within specified tolerances.


5.     Antenna mount & drive system for the 12 m Preloaded Parabolic Dish
       Antenna:

       On behalf of the Raman Research Institute, a firm in Bangalore, has made
preliminary design calculations for mount and drive system of the 12 m antenna.       For
the elevation drive of an Alt-Azimuth system, two different concepts have been
considered : (i) Ball screw drive (ii) Sector Gear drive. For the azimuth drive either (a)
four point contact Slew Ring or (b) Wheel & Track arrangement have been examined.
For the RRI mount, it is proposed to freeze the design by July 2002 using Sector Gear
for elevation and either Slew Ring or Wheel and Track for azimuth. The mount and the
drive are expected to be fabricated by early 2003 and will then be integrated with the 12
m preloaded parabolic dish. Servo motors have been purchased and electronic drive
units are already being assembled at RRI. A Cassegrain system is being developed by
RRI for a survey of Methanol masers near 6.7 GHz, which would also allow testing of
the performance of the 12 m PPD antenna by the middle of 2003.


       Preliminary cost estimate of the backup structure and reflecting surface of the 12
m dish, its mount and drive system, including gear boxes and encoders, are given in
Table-2. It may be noted that these are rough estimates considering mass production
and for location in a Western country. More accurate estimates will be made by the
middle of 2003. The present estimates for the cost of mount and drive system seems to
be about two times higher than that of the 12 m PPD dish including reflector panels.
However, mechanical design has not been optimized.

6.     Strawman’s Design for the Antenna System of SKA using 8343 Nos.of


                                             14
       12 m PPDs

       For meeting the major specifications of SKA, it is proposed to use a total of 8343
PPD antennas of 12 m diameter placed in a suitable array of about 500 km in extent or
larger as may be recommended by the scientific, antenna array and correlator groups.
Each station will consist of a closely placed 2-dimensional array of 12 m dishes, e.g. if
103 stations are decided, each station will consist of an array of 9 x 9 dishes of 12 m
diameter so that the total number of dishes being 8343. Alternatively, one may choose
102 stations of 7 x 7 dishes of 15 m diameter with the total number of dishes being
4998. About 30% of these antennas may be placed in a closely spaced central array of
a suitable design, as may be considered optimum for meeting some of the scientific
objectives of SKA.


       In order to cover the frequency range from 0.15 to 10 GHz and also to get nearly
the same E & H beamwidth for achieving good polarization characteristics, one may
place four log periodic antennas in a quad arrangement at the primary focus of the 12 m
dishes. A Cassegrain design may be possible if one restricts the frequency range
suitably, as is being adopted for the 6.1 m offset parabolic dishes of the Allen Telescope
Array (ATA) of the SETI institute. For the proposed 12 m dishes of SKA, it should be
possible to adopt the basic design of the feed and receiver system of ATA.




       In Fig. 4 is illustrated a possibility of extending operation of the 12 m or 15 m
PPD antennas from about 30 MHz to 22 GHz as may be required for SKA. As stated
earlier, one may use accurate panels of metal sheets for the central 6 m diameter and a
Cassegrain feed for covering 5 GHz to 22 GHz, a primary feed of a quad of four log –
periodic array for 150 MHz to 5 GHz and active antennas on the periphery/ rim of the
PPDs for covering 30 MHz. to 150 MHz.


       As described in Section-5, a 12 m dish has been fabricated at the Raman
Research Institute with panels of 6mm x 6mm x 0.55 mm having deviation of 2 mm rms
from the required parabola. In Table-2 are presented expected performance of the 12




                                           15
m PPD antennas. In Table-3 are given a rough cost analysis of the 12 m dish. Cost
estimates given in Tables-2 & 3 are tentative and will be improved by mid 2003.


       The lowest computed frequency of vibrations or elastic modes of the PPD
according to the finite element analysis made by Professor Joshi of IIT, Bombay is
around 1.5 Hz. However, the measured frequency is about 1.2 Hz. During the windy
days at Bangalore, it is planned to measure the effect of wind on the PPD. If a higher
value of frequency is required, we may connect some additional tubular members from
the lower side of the hub to a suitable location (say 6 m diameter circle) of the 12 m
PPD.


       In Table-4 we have made a comparison of the "SKA design goals" with the
achievable specifications of the Strawman’s design using 12 m dishes. It may be seen
that if parabolic dishes are selected for the antenna elements of SKA, they will meet all
the design goals for the SKA (as have been summarized in the Science Document for
SKA), except No. of instantaneous beams. However, it should be possible to make
sub-arrays of the 12 m dishes, pointing in different directions. Further, within the primary
beams of each 12 m dish, the correlator system will provide the full coverage.
Advantages of using parabolic dishes for SKA is discussed in Section-7.

7.     Discussions
7.1    Advantages of Preloaded Parabolic Dishes


       As is widely known that parabolic dishes have several advantages for use in a
       radio telescope. Some of these are listed below:-
       •       Steerability over all the sky.
       •       Wide frequency coverage ( < 100 MHz to ~ 22 GHz.).
       •       Wide bandwidths are possible which will allow dynamic channel
               assignments for minimizing RFI.
       •       Sidelobes of each 12 m antenna are likely to be about - 20 dB and
               further a null can be produced in specified directions by suitable phasing
               of the array of 9 x 9 antennas at each station or of few thousand
               antennas in the central array.


                                                16
         •           Good Polarization Characteristics.
         •           Less Complex electronics than phased arrays which may allow:
                     -      Lower system temperature,
                     -      Better phase and gain stability resulting in better calibration
                            capabilities, which is extremely important for achieving the
                                       6
                            required 10 dynamic range at 1.4 GHz.


7.2      Antenna element for SKA


         A brief comparison of different concepts being developed by the SKA partners
         was presented by the Antenna Working Group at the SKA workshop held at
         Berkely in July 2001. In order to make a relative comparison of these concepts,
         it is suggested that we may consider a "Figure of merit", F, for each concept:


                                                                  2
         F1 = [ sky coverage (δ) x Freq. coverage] / [(cost/m ) . Tsys ]


         An additional parameter, F2, will be the no. of instantaneous beams, which will
         increase the cost of SKA. Therefore, the total cost of the antenna and receiver
         system will have to be considered, along with F1 & F2, and some other factors
         such as achievable dynamic range, RFI susceptibility, maintenance aspects, etc.


8.       Conclusions


      Over the last few years, considerable work has been done by NCRA-TIFR for
developing the novel concept of the preloaded parabolic dish antenna.           A detailed
design of the 12 m PPD antenna has been made.             RRI has fabricated the 12 m dish
and has also developed lightweight panels for the reflecting surface. A firm in Bangalore
is developing a design for the mechanical drive system. The full 12 m dish including the
servo system and electronics is expected to be operational by the middle of 2003. An
approximate cost estimate has been made for the 12 m PPD antennas including
mechanical and servo system. The cost of the antenna system of SKA for achieving Tsys
             4   2   -1                                       6
= 2 x 10 m K at 1.4 GHz will be about US $ 500 x 10 using 8333 dishes of 12 m or




                                                 17
5000 dishes of 15 m diameter.        Better estimates will be made by mid 2003.        As is
known, the antenna system may form about 50 or 60% of the cost of SKA.


      Parabolic dishes offer an attractive option for SKA. The cost of the antenna system
is likely to be optimised if the PPD antennas described in this report are employed for
SKA.


9.        Acknowledgements


          We thank S.C. Tapde & M.N. Karthikeyan of NCRA-TIFR, N.V.G. Sarma, M.
Modgekar and C. Md. Ateequella of RRI,             D. Satyanarayan formerly of M/s. Tata
Consulting Engineers and H.S. Kedlaya of M/s. S.K. Engineering for valuable
discussions and contributions.     We also thank Prof. Ashok Joshi of the Indian Institute
of Technology, Mumbai for a finite element analysis & design of the 12 m & 25 m
dishes.


10.        References


     1.      Taylor, A.R., and Braun, R., "Science with the Square Kilometer Array",
             March 1999, University of Calgary, Canada.


     2.      Cohen, E., "Large Steerable Radio Antennas – Climatological and
             Aerodynamics considerations", Annals of the New York Academy of
             Sciences, 116, Art. 1, 1964.
     3.      Swarup, G., Ananthakrishnan, S., Kapahi, V.K., Rao, A.P., Subrahmanya,
             C.R., and Kulkarni, V.K., "The Giant Metrewave Radio Telescope", Current
             Science, 60, pp. 95-105, 1991.
     4.      Swarup, G., " An International Radio Telescope for Radio Astronomy",
             Current Science, 60, pp. 106-108, 1991.




                                              18
Hck/Swarup/SKA




                 19
Table 1 :            Parameters of the Preloaded Parabolic Dishes of 12 m and 25 m
diameter.




Sr. No.       Item                                    Units      Diameter             Diameter
                                                              -----------------   -----------------
                                                                    12 m                25 m *
                                                          2
   1.         Area (Physical)                          m         113                  491
   2.         No. of Radial Spokes                     -          24                    36
   3.         Hub Diameter                             m          4.0                   7.0
   4.         Wire Mesh Size                           mm     6 x 6 x 0.55        10 x 10 x 0.55
   5.         Solidity                                 %          22                   28
   6.         Maximum mass at focus ( feed             kg         50                  200
              & electronics)
   7.         Maximum mass of full dish            Tonnes          2.7                 14.0
              excluding gear drive system
              and antenna mount
   8.         Survival wind velocity                kmph           150                 140
   9.         Wind Force (horizon)                 Tonnes           2.7                 13
  10.         Wind Torque About Elevation            t-m            2.0                 19
              Axis
  11.         Dead Load Torque about                   t-m         4.7                   42
              elevation (before balancing)


          •          Values for 25 m dish are tentative




                                                 20
Table -2 : Approximate performance parameters for a set of 8333 dishes of 12 m
          diameter using 4 log-periodic feeds & pulsed cooled receiver, similar to that
          of the Allen Telescope Array(ATA).


f       λ              η**      Ae’     Aeff = 8333xAe’        Tsys**   Aeff/Tsys    Beam-
                       (effi-                                                        Width
                                   2        5    2                         2
        (mm)           ciency (m )      (10 m )                (K)      (M /K)       (deg.)
0.15    2000           0.50        56       4.67                350      1333        11.65
0.30    1000           0.60        68       5.67                 90      6296         5.83
0.60        500        0.65        73       6.08                 40     15208         2.91
1.42        210        0.64        72       6.00                 30     20000         1.22
5.00         60        0.50        56       4.67                 45     10370         0.35
10.00        30        0.25        28       2.33                 60       3888        0.17



* Assuming (a) Antenna aperture efficiency due to illumination of 0.5 at 150MHz and
               0.65 at higher frequencies.


              (b) rms error of the reflecting surface = 2mm.

              (c) Reflectivity leakage of the wire mesh of size 6mm x 6mm x
                  0.55mm size as a function of frequency, based on calculations.
                                                                          -2.6K
 ** Assuming galactic background temperature of 50 x (f(MHz)/300) , ATA type
receiver but with a primary feed of 4 log-periodic antennas and ground leakage for the
wire mesh of size 6mm x 6mm x 0.55mm.




                                            21
Table 3 :      Comparison of the "SKA Design Goals" with the achievable
specifications
               of the Strawman design using Preloaded Parabolic Dishes of 12 m
               diameter.


Item                             Specifications           12 m dish         Notes
Frequency Range                  0.15-20 GHz              0.15-10 GHz        1
Image field view                 1 square deg. at 1.4     1.22 deg.          2
                                 GHz
Number of Instantaneous          At least 100             Sub-arrays         3
beams
Angular resolution               0.1 arcsec at 1.4 GHz    Yes                4
                                       8
Number of spatial pixels          10                      Yes                5
Surface brightness sensitivity   1K at 0.1 arcsec         Yes                5
                                 (continuum)
Instantaneous bandwidth          (0.5+0.2 x frequency)    Yes                5
                                 GHz
                                     4
Number of spectral channels      10                       Yes                5
                                                  -4 2
Sensitivity                      Aeff/Tsys = 2x10 m       Yes                -
                                   1
                                 K
                                     6
Image dynamic range              10 at 1.4 GHz            Yes                6
Polarization purity              -40 dB                   Yes                7


NOTES :

   1.      20 GHz possible if the central 6 m part of the 12 m dish is made of Aluminum
           sheets (solid or perforated).
   2.      1 degree field of view for a 15 m dish.
   3.      100 instantaneous beams not possible if dishes used (however, see Section-
           6)
   4.      Resolution will depend on overall extent of SKA ; an array of more than 500
           km in extent will be required.
   5.      These parameters will depend upon design of the receiver and correlator
           system.
   6.      Requires careful study by correlator and image analysis group.
   7.      Each dish with primary feed will give polarization purity of only about -25dB
           but it may be possible to get -40dB by suitable electronics for an array of 9 x
           9 12 m dishes.




                                           22
     Table 4 : Preliminary cost estimate for 12 m Preloaded Parabolic Dish Antenna
     including the Mount and Drive System.


Item                                                                  Cost
                                                                     (US $)
1. Fabrication and erection of preloaded backup structure
    of 12 m PPD antenna :

     (a)   Cost of hub including fabrication (660 kg:M.S. Plate)    1200
     (b)   Cost of Joints (clamps & bolts) : 500 kg                 1000
     (c)   Cost of tubular structural members of PPD: 1220 kg       2000
     (d)   Cost of S.S. Mesh & fabrication of Panels : 320 kg       3200
     (e)   Labour Cost for Assembly of hub, tubular structural      6400
           members of PPD, Joints and wire mesh panels.
     (f)   Central dish                                              1200
     (g)   Miscellaneous                                             1000
                                                                   ----------
                                                                    16000
                                                                   =====

2. Mount & Mechanical Drive System
     (a) Elevation drive including gear boxes                        8000
     (b) Azimuth drive including gear boxes                         14000
     (c) Mount & foundation                                          8000
     (d) Miscellaneous                                               4000
                                                                   ---------
                                                                    34000
                                                                   ---------
3.     Servo System including encoders                              10000
                                                                   =====
                                    Total US $                      60000




                                             23
                                                          1


Fig 1: Basic principle of a preloaded structural member supported by an anchor member.
Fig 2: Details of the 12 m preloaded parabolic dish (PPD) antenna.
Fig 3: A sketch illustrating the geometry of one of the straight radial structural members of the 12m
dish clamped on the hub at an angle of 12.5o to the plane of the hub and then bent elastically so as to
lie closely to the required parabolic curve.
                                                                    Wire mesh panels
30 MHz-150 MHz                                                      6mm*6mm*0.55mm
Active Antenna Phased
Array (LOFAR Design)




                                                                  Dish made of solid
                                                                  Aluminium sheets

                                                              Array of 4 * log periodic antennas
6mm*6mm*0.55mm wire mesh
                                                                     Cassegrain reflector




                                                                 Al Panels or 6m formed dish
                              Hub                  Horn


    Fig. 4: Proposed sketch of a 12m preloaded parabolic dish with (a) solid reflector of 6m
    diameter with Cassegrain system for covering 5–22 GHz; (b) wire mesh 6m to 12m; with
    primary feed to cover 0.15 GHz to 5 GHz and (c) active antennas on the rim of the dish for
    30MHz to 150MHz.

				
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